Then, all Commodores and Admirals and Starbase personnel wore that "flower" insignia.

But then, it also became the insignia of the USS Lexington (that's the only starship we've seen that has this insignia).

But, isn't Wesley the only officer whose insignia we get a good look at on the Lexington? I always thought that he wore the flower because he was normally assigned to starbase/space station, but he was in command of the battle fleet in wargames against the M5. If that was the case, then we never see the Lexington insignia. Now the question would then become, where was the captain of the Lexington, and that I have no answer for.

Notice Commodore Wesley's high command chair (neither Exeter or Defiant had this chair), looks like the Lexington might be Starfleet's flagship (in the mirror universe, ISS Enterprise apparently is the flagship there)

Bob

Well, the high-back could just be a normal variant, too, with no special significance, couldn't it?

__________________“A life is like a garden. Perfect moments can be had, but not preserved, except in memory. LLAP” — Leonard Nimoy (1931-2015)